[en] In this survey we attempt to give a unified presentation of a variety of
results on the lifting of valid inequalities, as well as a standard procedure com-
bining mixed integer rounding with lifting for the development of strong valid
inequalities for knapsack and single node flow sets. Our hope is that the latter can
be used in practice to generate cutting planes for mixed integer programs.
The survey contains essentially two parts. In the first we present lifting in a very
general way, emphasizing superadditive lifting which allows one to lift simultane-
ously different sets of variables. In the second, our procedure for generating strong
valid inequalities consists of reduction to a knapsack set with a single continuous
variable, construction of a mixed integer rounding inequality, and superaddilifting. It is applied to several generalizations of the 0-1 single node flow set.